ESAT Notes and Formula Decks

Module Resources (Clean View)

Compact formulas, prep routines, and a short runway plan. Pick a module, expand its card, then jump to walkthroughs when you want worked examples.

View Spec Walkthroughs ESAT Hub

Physics Formula Pack

  • $$s = ut + \frac{1}{2}at^2$$
  • $$v^2 = u^2 + 2as$$
  • $$v = u + at$$
  • $$F = ma$$
  • $$p = mv$$
  • $$F \Delta t = \Delta p$$
  • $$E_k = \frac{1}{2}mv^2$$
  • $$E_p = mgh$$
  • $$W = Fd \cos(\theta)$$
  • $$V = IR$$
  • $$P = IV = I^2R = \frac{V^2}{R}$$
  • Series/parallel R rules
  • $$v = f\lambda$$
  • $$f_n = \frac{nv}{2L}$$
  • Intensity $\propto \frac{1}{r^2}$

Maths 1 Formula Pack

  • Log laws: $$\ln(ab) = \ln a + \ln b$$, $$\ln(a^k) = k \ln a$$
  • Quadratics: solutions of $$ax^2 + bx + c = 0$$ via discriminant $$b^2 - 4ac$$
  • Trig identities: $$\sin^2 x + \cos^2 x = 1$$, $$\tan x = \frac{\sin x}{\cos x}$$, $$\sin(A \pm B)$$ formulas
  • Differentiation: $$\frac{d(x^n)}{dx} = nx^{n-1}$$, $$\frac{d(\ln x)}{dx} = \frac{1}{x}$$, $$\frac{d(e^x)}{dx} = e^x$$
  • Integration: $$\int x^n dx = \frac{x^{n+1}}{n+1} + C$$ ($$n \neq -1$$), $$\int e^x dx = e^x + C$$

Maths 2 Formula Pack

  • Geometric: $$S_{\infty} = \frac{a}{1-r}$$ for $$|r| < 1$$
  • Binomial: $$(1+x)^n = 1 + nx + \frac{n(n-1)}{2}x^2 + \dots$$ ($$|x| < 1$$)
  • Matrices: $$\det \begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc$$; inverse $$= \frac{1}{ad-bc} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$$
  • Complex: $$z = re^{i\theta}$$; modulus $$r$$, argument $$\theta$$; Euler: $$e^{i\theta} = \cos\theta + i\sin\theta$$
  • Vectors: $$\mathbf{a} \cdot \mathbf{b} = |\mathbf{a}| |\mathbf{b}| \cos(\phi)$$ ; projection of $$\mathbf{a}$$ on $$\mathbf{b} = \frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{b}|}$$

Prep Notes

  • No calculator; practise mental arithmetic and clean algebra.
  • Check units and proportionality on every numeric item.
  • Carry a one-page formula sheet; rewrite it weekly from memory.
  • Use walkthroughs to copy the structure, then re-derive cold.
  • Target 90 seconds per item in drills; always guess if unsure.

Study Rhythm

  • Rotate daily: Physics set, Maths 1 set, Maths 2 set.
  • Keep a mistake log tagged by topic and root cause.
  • End sessions with a mixed mini-set to mimic paper shuffle.
  • Refresh formulas and key identities before each block.

Exam Moves

  • First pass: quick wins, skip anything over 90 seconds.
  • Eliminate impossible options; estimate from bounds.
  • Re-read stems for qualifiers (always, must, could).
  • Order-of-magnitude and sign checks before committing.

6-Week Runway (Light)

Weeks 1-2

  • • Rebuild fundamentals (algebra, trig, kinematics).
  • • Make formula flashcards; rewrite twice a week.
  • • 20-30 untimed questions per day.

Weeks 3-4

  • • Timed sets (30-40 mins), mark and rework.
  • • One mixed paper-equivalent weekly.
  • • Update mistake log and flashcards.

Weeks 5-6

  • • Two full timed papers weekly.
  • • Targeted drills on weak tags.
  • • Lock routine: sleep, food, and timing.

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